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Semi-Analytic Method for CDO : Gaussian Copula
  • Credit models and the crisis, or: How I learned to stop worrying and love the CDOs We follow a long path for Credit Derivatives and Collateralized Debt Obligations (CDOs) in particular, from the introduction of the Gaussian copula model and the related implied correlations to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time. En passant, we also illustrate the implied copula, a method that can consistently account for CDOs with different attachment and detachment points but not for different maturities. The discussion is abundantly supported by market examples through history. The dangers and critics we present to the use of the Gaussian copula and of implied correlation had all been published by us, among others, in 2006, showing that the quantitative community was aware of the model limitations before the crisis. We also explain why the Gaussian copula model is still used in its base correlation formulation, although under some possible extensions such as random recovery. Overall we conclude that the modeling effort in this area of the derivatives market is unfinished, partly for the lack of an operationally attractive single-name consistent dynamic loss model, and partly because of the diminished investment in this research area. , D.Brigo, A.Pallavicini, R.Torreseti (2009)
  • A simple dynamic model for pricing and hedging heterogenous CDOs , A. V. Lopatin (2008)
  • Credit Portfolio Modelling with Elliptically Contoured Distributions , C. Prestele (2007)
  • Credit Risk Models IV: Understanding and pricing CDOs , A.Elizalde (2006)
  • Credit Risk: Modeling and Application , Z.Wei (2006)
  • Valuing Credit Derivatives Using an Implied Copula Approach , J. Hull, A. White (2006)
  • Extensions to the Gaussian copula: random recovery and random factor loadings This paper presents two new models of portfolio default loss that extend the standard Gaussian copula model yet preserve tractability and com- putational efficiency. In one extension, we randomize recovery rates, explicitly allowing for the empirically well-established effect of inverse correlation between recovery rates and default frequencies. In another extension, we build into the model random systematic factor loadings, effectively allowing default correlations to be higher in bear markets than in bull markets. In both extensions, special cases of the models are shown to be as tractable as the Gaussian copula model and to allow efficient calibration to market credit spreads. We demonstrate that the models – even in their simplest versions – can generate highly significant pricing effects such as fat tails and a correlation “skew” in synthetic CDO tranche prices. When properly calibrated, the skew effect of random recovery is quite minor, but the extension with random factor loadings can produce correlation skews similar to the steep skews observed in the market. We briefly discuss two alternative skew models, one based on the Marshall- Olkin copula, the other on a spread-dependent correlation specification for the Gaussian copula. , L. Andersen, J. Sidenius (2005)
  • Valuation of a CDO and an nth to Default CDS Without Monte Carlo Simulation , J.Hull, A.White (2003)
  • Basket Default Swaps, CDOs and Factor Copulas , J.-P. Laurent, J. Gregory (2003)

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